Most likely your offer wasn't accepted due to the terms of your offer. As you are well aware, the inventory in Jackson is very low. As such, you need to be very aggressive with your initial offer to show the seller that you are a serious buyer. The sellers are of course going to take the offer that is stronger. Your agent should be able to tell you the reason your offers are being rejected.
It is currently a Seller's market and many homes in the area are getting multiple offers. Some homes are selling over asking price. None of us can answer why your offer was not accepted without knowing the particular situation, It really depends on the circumstances of the sale. Were you negotiating on a short sale or a normal sale? On short sales, if you make an offer too low or have many contingencies your offer more than likely will get rejected. If it is not a short sale and the house had multiple offers on it, your realtor should have been made aware of that by the listing agent so that you could have negotiated more aggressively. Have your realtor find out why your offer was not accepted. If you really want the house you can always state that you would like to be the back up contract in case the other buyer changes their mind. It sometimes happens.
I would have to agree with most of the answers already given. The first place you should be going is to your agent. He or She should be able to tell you what the problem is. Like Caroline says it may be financing or your terms. I don't know if you have any contingencies. All of these could be the reason that they have rejected your offer. Good luck to you.
What did your Realtor tell you? Sometimes the price isn't the problem it is the terms. Financing, earnest money, time to closing etc. Be sure to ask your realtor and get all the answers so the next time you make an offer you have all the information.
I agree with james. Your agent would and should have all those answers for you. There might of been a bidding war and someone could of came in higher then asking price. But I would definately contact her. Good luck
PLEASE, PLEASE, PLEASE ask your agent to contact the list agent and find out. Possibly based on the offer terms? Possible they feel your loan has no chance of being approved? Possible they're looking for an all cash buyer? Possible they have many offers?